Need some help with this... doesn't seem to be a decent example in my book. Appreciate any help!

May 4th 2010, 09:23 AM

tonio

Quote:

Originally Posted by gralla55

Need some help with this... doesn't seem to be a decent example in my book. Appreciate any help!

1) Apply the transformation T to each and every element of E and write the result as a linear combination of E itself;

2) Take the transpose , if you apply transformations from the left and vectors from the right), or directly (otherwise) the coefficients matrix of the above: this is .

For example:

...

So the first two columns of are (or the first two rows if you write the map on the right of the vector).

Tonio

May 6th 2010, 02:03 AM

gralla55

Thanks for your reply! But how do you get:

T(x) = -2 + 2x ? Shouldn't that just equal 2?

Thanks again.

May 6th 2010, 03:26 AM

HallsofIvy

Quote:

Originally Posted by gralla55

Thanks for your reply! But how do you get:

T(x) = -2 + 2x ? Shouldn't that just equal 2?

Thanks again.

Yes, that must have been a typo. Since T(f)= f(x)+ f(2- x), T(x)= x+ (2- x)= 2.

May 6th 2010, 04:08 AM

gralla55

In that case 2 is the answer for all four. And a linear combination would just be every element of E times 1/2 times each column vector? And won't the transpose of this matrix is the same as the matrix itself?

May 6th 2010, 05:09 AM

tonio

Quote:

Originally Posted by gralla55

In that case 2 is the answer for all four.

Why? ...

Tonio

And a linear combination would just be every element of E times 1/2 times each column vector? And won't the transpose of this matrix is the same as the matrix itself?

.

May 6th 2010, 05:18 AM

gralla55

Don't you just substitute the "x" for "x^2" ? I don't see why the ^2 suddenly goes outside the parantheses. But of course, I might be wrong here...